Use the image to answer the question.

Question

A quadrilateral upper A upper B upper C upper D. Two diagonals connect vertices upper A to upper C and upper B to upper D. The point of intersection is upper O.

In a proof that the diagonals of rectangle ABCD
are congruent, which statement comes just after the statements that AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
, AB¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯
, and ∠DAB≅∠CBA
?

(1 point)
Responses

△DAB≅△DOC
triangle upper A upper O upper D congruent to triangle upper C upper O upper B

△DAB≅△AOB
triangle upper A upper D upper B congruent to triangle upper C upper B upper D

△DAB≅△CBA
triangle upper A upper O upper B congruent to triangle upper D upper O upper C

△DAB≅△DAO

Answer 1

In the context of proving that the diagonals of rectangle ABCD are congruent, after stating that \( AD \cong BC \), \( AB \cong AB \), and \( \angle DAB \cong \angle CBA \), we can use the criteria for triangle congruence.

The appropriate statement that follows would be:

△DAB≅△CBA

This is because we are showing that triangles DAB and CBA are congruent by using the Side-Angle-Side (SAS) congruence criteria. Once we establish that these triangles are congruent, it logically leads to the conclusion that \( AC \cong BD \), which confirms that the diagonals are congruent.

Thus, the correct response is:

△DAB≅△CBA (triangle upper A upper O upper B congruent to triangle upper D upper O upper C)